# Aryabhatiya

# ĀRYABHATĪYA

**ĀRYABHATĪYA** The *Āryabhatīya*, the astronomical text written by Āryabhata (born 476), is one of the landmarks of the history of astronomy. The *Āryabhatīya* is divided into four parts. The first part provides basic definitions and important astronomical parameters. It mentions the number of rotations of Earth and the revolutions of the sun, moon, and the planets in a period of 4,320,000 years. This is a partially heliocentric system because it presents the rotation information of the planets with respect to the sun. The second part deals with mathematics. The third part deals with the determination of the true position of the sun, the moon, and the planets by means of eccentric circles and epicycles. The fourth part deals with planetary motions on the celestial sphere and gives rules relating to various problems of spherical astronomy.

The notable features of the *Āryabhatīya* are Ā ryabhata's theory of Earth's rotation and his excellent planetary parameters based on his own observations made around a.d. 512, which are superior to those of others. He made fundamental improvements over the prevailing *Sūrya-siddhānta* techniques for determining the position of planets. Unlike the epicycles of Greek astronomers, which remain the same in size at all places, Āryabhata's epicycles vary in size from place to place. Āryabhata expressed relativity of motion very effectively thus: "Just as a man in a boat moving forward sees the stationary objects (on the shore) as moving backward, just so are the stationary stars seen by the people on earth as moving exactly towards the west."

Āryabhata took the sun, the moon, and the planets to be in conjunction in zero longitude at sunrise at Lanka on Friday, 18 February 3102 b.c. In a period of 4.32 million years, the moon's apogee and ascending node too are taken to be in conjunction with the planets. This allowed him to solve various problems using whole numbers.

The theory of planetary motion in the *Āryabhatīya* is based on the following ideas: the mean planets revolve in geocentric orbits; the true planets move in eccentric circles or in epicycles; planets have equal linear motion in their respective orbits. The epicycle technique of Āryabhata is different from that of the Greek astronomer Ptolemy and it appears to be derived from an old Indian tradition.

Āryabhata made important innovations on the traditional Sūrya-siddhānta methods for the computation of the planetary positions. The earlier methods used four corrections for the superior planets and five for the inferior planets; Āryabhata reduced the number of corrections for the inferior planets to three and improved the accuracy of the results for the superior planets.

Āryabhata considers the sky to be 4.32 million times the distance to the sun. He and his followers believed that beyond the visible universe illuminated by the sun and limited by the sky is the infinite invisible universe. Rather than taking the universe to be destroyed at the end of the "Brahmā's day" of 4.32 billion years, he took Earth to go through expansion and contraction equal to one *yojana* (approximately 7.5 miles [12 km] according to Āryabhata; 9 miles [14.5 km] by the mainstream Indian tradition).

*Āryabhatīya'*s mathematics includes the decimal place-value system, various problems of arithmetic and geometry, sums of arithmetic series, and the solution of the linear indeterminate equation using the pulverizer method.

Many passages in the *Brāhma-sphuta-siddhānta* of Brahmagupta (born 598) are strikingly similar to that of the *Āryabhatīya*, showing the influence of Āryabhata. His commentator Bhāskara I (seventh century) declared that Āryabhata's theories were the best, and they were widely thought to be so all over India, especially in Kerala.

*Subhash Kak*

## BIBLIOGRAPHY

Billard, R. *L'Astronomie Indienne*. Paris: École Française d'Extrême Orient, 1971.

Shukla, K. S., and K. V. Sarma. Āryabhatīya *of Āryabhata*. New Delhi: Indian National Science Academy, 1976.

Thurston, H. *Early Astronomy.* New York: Springer-Verlag, 1994.

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**Aryabhatiya**